Two Facebook users have begun a class-action lawsuit that alleges the social network's "private" messaging system is a lie.

The pair, Matthew Campbell and Michael Hurley, reckon each of the website's estimated 166 million US users should get a payday of up to $10,000 apiece as compensation.

The suit, filed in California, states that Facebook explicitly promises that the content of private messages won't be shared with third parties. But, it claims, if a URL is included in a message then Facebook's software automatically parses the web address and the content of the message to hone its targeted advertising.

"Facebook misleads users into believing that they have a secure, private mechanism for communication – Facebook's private messaging function – when, in fact, Facebook intercepts and scans the content and treats portions of that content no differently than a public 'Like' or post, broadcast openly across the Internet," the court filing claims.

"Further, the purpose for the invasive scanning of these purportedly 'private' messages is not meant for the benefit of users, but rather is a mechanism for Facebook to surreptitiously gather data in an effort to improve its marketing algorithms and increase its ability to profit from data about Facebook users."

The suit alleges that while users are kept in the dark over private message processing, the social network's "web crawlers" notify third parties when their websites are referred to in messages by URL – just as though they had received public "Likes" on their web pages.

The plaintiffs say this behavior was exposed by two separate security researchers last year and as a result they are asking for a class-action case to be brought against Facebook. In August, Swiss researchers at High-Tech Bridge said they spotted the practice, and were backed in October by Ashkan Soltani, formerly an FTC investigator and now an independent security consultant.

The suit asks that any user who has sent messages with URLs in them should be able to claim up to $10,000 – meaning the potential payout by Facebook could be as high as $166bn, or about $30bn more than the firm's market capitalization today.